When we write a number as the sum of the place value of its digits, the number is called the stale form, and when we write a number with digits, the number is called the short form.

Extended form of a number:

If we write 3476, the number really means 3000 + 400 + 70 + 6. This means that we have expanded the number to show the value of each of its digits.

The expanded form of a number is the method of expressing the number as the sum of the place value of all its digits.

**For example,**

Look at number 2815

2815 = 2000 + 800 + 10 + 5

There are three ways to write the advanced form. There are three ways to write the advanced form for a specific number.

Examples of the expanded form of a number:

**1.** Write the extended form for 43,257.

**Solution:**

1^{st} Way: 4 tens of thousands + 3 thousand + 2 hundred + 5 tens + 7 ones

2^{nd} Way: 4 × 10000 + 3 × 1000 + 2 × 100 + 5 × 10 + 7 × 1

3^{approx} Way: 40000 + 3000 + 200 + 50 + 7

**2.** Write the advanced form for 14,080.

**Solution:**

14,080 = 1 ten thousand + 4 thousand + 8 tens [Note: We do not write the place value for

hundreds and ones as these places are filled with zero.]

or 1 × 10000 + 4 × 1000 + 8 × 10

or 10000 + 4000 + 80

Standard form of a number / short form of a number:

The standard form of a number is a way of expressing the expanded form in numbers.

For example, the standard form is 7000 + 400 + 10 + 1 = 7411

Examples of extended form and short form of a number:

**3rd** Write the short form for the specified extended forms.

(i) 8 tens of thousands + 6 hundred + 6 tens + 3 ones

(ii) 9 × 10000 + 7 × 1000 + 4 × 10 + 2

(iii) 40000 + 3000 + 900 + 70 + 8

**Solution:**

(i) 8 tens of thousands + 6 hundred + 6 tens + 3 ones (ii) 9 × 10000 + 7 × 1000 + 4 × 10 + 2 (iii) 40000 + 3000 + 900 + 70 + 8 |
80663 97042 43978 |

Questions and answers about the extended form and the standard form of a number:

**I. Write in expanded form:**

(i) 5896

(ii) 3817

(iii) 6399

(iv) 1357

(v) 3434

(vi) 5690

**Reply:**

**I.** (i) 5000 + 800 + 90 + 6

(ii) 3000 + 800 + 10 + 7

(iii) 6000 + 300 + 90 + 9

(iv) 1000 + 300 + 50 + 7

(v) 3000 + 400 + 30 + 4

(vi) 5000 + 600 + 90 + 0

**II. Write in the standard form:**

(i) 2000 + 900 + 90 + 9

(ii) 8000 + 200 + 50 + 3

(iii) 1000 + 400 + 50 + 2

(iv) 4000 + 300 + 9

(v) 6000 + 900 + 80 + 4

**Reply:**

**II. **(i) 2999

(ii) 8253

(iii) 1452

(iv) 4309

(v) 6984

**3rd grade math lesson**

**From the extended form and short form of a number to the start page**

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